topical media & game development
student-ar-org-papervision3d-core-math-Matrix3D.ax
student-ar-org-papervision3d-core-math-Matrix3D.ax
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package org.papervision3d.core.math
{
import org.papervision3d.Papervision3D;
* The @ax-student-ar-org-papervision3d-core-math-Matrix3D class lets you create and manipulate 4x3 3D transformation matrices.
public class @ax-student-ar-org-papervision3d-core-math-Matrix3D
{
* X O O O
* O O O O
* O O O O
public var n11 :Number;
* O X O O
* O O O O
* O O O O
public var n12 :Number;
* O O X O
* O O O O
* O O O O
public var n13 :Number;
* O O O X
* O O O O
* O O O O
public var n14 :Number;
* O O O O
* X O O O
* O O O O
public var n21 :Number;
* O O O O
* O X O O
* O O O O
public var n22 :Number;
* O O O O
* O O X O
* O O O O
public var n23 :Number;
* O O O O
* O O O X
* O O O O
public var n24 :Number;
* O O O O
* O O O O
* X O O O
public var n31 :Number;
* O O O O
* O O O O
* O X O O
public var n32 :Number;
* O O O O
* O O O O
* O O X O
public var n33 :Number;
* O O O O
* O O O O
* O O O X
public var n34 :Number;
* O O O O
* O O O O
* O O O O
* X O O O
public var n41 :Number;
* O O O O
* O O O O
* O O O O
* O X O O
public var n42 :Number;
* O O O O
* O O O O
* O O O O
* O O X O
public var n43 :Number;
* O O O O
* O O O O
* O O O O
* O O O X
public var n44 :Number;
// temp objects to save constant instantiation of objects.
static private var temp : @ax-student-ar-org-papervision3d-core-math-Matrix3D = @ax-student-ar-org-papervision3d-core-math-Matrix3D.IDENTITY;
static private var n3Di : Number3D = Number3D.ZERO;
static private var n3Dj : Number3D = Number3D.ZERO;
static private var n3Dk : Number3D = Number3D.ZERO;
// _________________________________________________________________________________ @ax-student-ar-org-papervision3d-core-math-Matrix3D
* The @ax-student-ar-org-papervision3d-core-math-Matrix3D constructor lets you create @ax-student-ar-org-papervision3d-core-math-Matrix3D objects.
*
* @param args The values to populate the matrix with. Identity matrix is returned by default.
public function @ax-student-ar-org-papervision3d-core-math-Matrix3D( args:Array=null )
{
reset(args);
//trace("new matrix");
}
// sets the properties of the Matrix without creating a new one.
public function reset( args:Array = null) : void
{
if( ! args || args.length < 12 )
{
n11 = n22 = n33 = n44 = 1;
n12 = n13 = n14 = n21 = n23 = n24 = n31 = n32 = n34 = n41 = n42 = n43 = 0;
}
else
{
n11 = args[0]; n12 = args[1]; n13 = args[2]; n14 = args[3];
n21 = args[4]; n22 = args[5]; n23 = args[6]; n24 = args[7];
n31 = args[8]; n32 = args[9]; n33 = args[10]; n34 = args[11];
if( args.length == 16 )
{
n41 = args[12]; n42 = args[13]; n43 = args[14]; n44 = args[15];
}
else
{
n41 = n42 = n43 = 0;
n44 = 1;
}
}
}
// _________________________________________________________________________________ IDENTITY
public static function get IDENTITY():@ax-student-ar-org-papervision3d-core-math-Matrix3D
{
//trace("Matrix.IDENTITY");
return new @ax-student-ar-org-papervision3d-core-math-Matrix3D
(
[
1, 0, 0, 0,
0, 1, 0, 0,
0, 0, 1, 0,
0, 0, 0, 1
]
);
}
// _________________________________________________________________________________ trace
public function toString():String
{
var s:String = "";
s += int(n11*1000)/1000 + "\t\t" + int(n12*1000)/1000 + "\t\t" + int(n13*1000)/1000 + "\t\t" + int(n14*1000)/1000 +"\n";
s += int(n21*1000)/1000 + "\t\t" + int(n22*1000)/1000 + "\t\t" + int(n23*1000)/1000 + "\t\t" + int(n24*1000)/1000 + "\n";
s += int(n31*1000)/1000 + "\t\t" + int(n32*1000)/1000 + "\t\t" + int(n33*1000)/1000 + "\t\t" + int(n34*1000)/1000 + "\n";
s += int(n41*1000)/1000 + "\t\t" + int(n42*1000)/1000 + "\t\t" + int(n43*1000)/1000 + "\t\t" + int(n44*1000)/1000 + "\n";
return s;
}
// _________________________________________________________________________________ OPERATIONS
public function calculateMultiply( a:@ax-student-ar-org-papervision3d-core-math-Matrix3D, b:@ax-student-ar-org-papervision3d-core-math-Matrix3D ):void
{
var a11:Number = a.n11; var b11:Number = b.n11;
var a21:Number = a.n21; var b21:Number = b.n21;
var a31:Number = a.n31; var b31:Number = b.n31;
var a12:Number = a.n12; var b12:Number = b.n12;
var a22:Number = a.n22; var b22:Number = b.n22;
var a32:Number = a.n32; var b32:Number = b.n32;
var a13:Number = a.n13; var b13:Number = b.n13;
var a23:Number = a.n23; var b23:Number = b.n23;
var a33:Number = a.n33; var b33:Number = b.n33;
var a14:Number = a.n14; var b14:Number = b.n14;
var a24:Number = a.n24; var b24:Number = b.n24;
var a34:Number = a.n34; var b34:Number = b.n34;
this.n11 = a11 * b11 + a12 * b21 + a13 * b31;
this.n12 = a11 * b12 + a12 * b22 + a13 * b32;
this.n13 = a11 * b13 + a12 * b23 + a13 * b33;
this.n14 = a11 * b14 + a12 * b24 + a13 * b34 + a14;
this.n21 = a21 * b11 + a22 * b21 + a23 * b31;
this.n22 = a21 * b12 + a22 * b22 + a23 * b32;
this.n23 = a21 * b13 + a22 * b23 + a23 * b33;
this.n24 = a21 * b14 + a22 * b24 + a23 * b34 + a24;
this.n31 = a31 * b11 + a32 * b21 + a33 * b31;
this.n32 = a31 * b12 + a32 * b22 + a33 * b32;
this.n33 = a31 * b13 + a32 * b23 + a33 * b33;
this.n34 = a31 * b14 + a32 * b24 + a33 * b34 + a34;
}
public static function multiply( a:@ax-student-ar-org-papervision3d-core-math-Matrix3D, b:@ax-student-ar-org-papervision3d-core-math-Matrix3D ):@ax-student-ar-org-papervision3d-core-math-Matrix3D
{
//trace("matrix.multiply");
var m:@ax-student-ar-org-papervision3d-core-math-Matrix3D = new @ax-student-ar-org-papervision3d-core-math-Matrix3D();
m.calculateMultiply( a, b );
return m;
}
public function calculateMultiply3x3( a:@ax-student-ar-org-papervision3d-core-math-Matrix3D, b:@ax-student-ar-org-papervision3d-core-math-Matrix3D ):void
{
var a11:Number = a.n11; var b11:Number = b.n11;
var a21:Number = a.n21; var b21:Number = b.n21;
var a31:Number = a.n31; var b31:Number = b.n31;
var a12:Number = a.n12; var b12:Number = b.n12;
var a22:Number = a.n22; var b22:Number = b.n22;
var a32:Number = a.n32; var b32:Number = b.n32;
var a13:Number = a.n13; var b13:Number = b.n13;
var a23:Number = a.n23; var b23:Number = b.n23;
var a33:Number = a.n33; var b33:Number = b.n33;
this.n11 = a11 * b11 + a12 * b21 + a13 * b31;
this.n12 = a11 * b12 + a12 * b22 + a13 * b32;
this.n13 = a11 * b13 + a12 * b23 + a13 * b33;
this.n21 = a21 * b11 + a22 * b21 + a23 * b31;
this.n22 = a21 * b12 + a22 * b22 + a23 * b32;
this.n23 = a21 * b13 + a22 * b23 + a23 * b33;
this.n31 = a31 * b11 + a32 * b21 + a33 * b31;
this.n32 = a31 * b12 + a32 * b22 + a33 * b32;
this.n33 = a31 * b13 + a32 * b23 + a33 * b33;
}
public function calculateMultiply4x4( a:@ax-student-ar-org-papervision3d-core-math-Matrix3D, b:@ax-student-ar-org-papervision3d-core-math-Matrix3D ):void
{
var a11:Number = a.n11; var b11:Number = b.n11;
var a21:Number = a.n21; var b21:Number = b.n21;
var a31:Number = a.n31; var b31:Number = b.n31;
var a41:Number = a.n41; var b41:Number = b.n41;
var a12:Number = a.n12; var b12:Number = b.n12;
var a22:Number = a.n22; var b22:Number = b.n22;
var a32:Number = a.n32; var b32:Number = b.n32;
var a42:Number = a.n42; var b42:Number = b.n42;
var a13:Number = a.n13; var b13:Number = b.n13;
var a23:Number = a.n23; var b23:Number = b.n23;
var a33:Number = a.n33; var b33:Number = b.n33;
var a43:Number = a.n43; var b43:Number = b.n43;
var a14:Number = a.n14; var b14:Number = b.n14;
var a24:Number = a.n24; var b24:Number = b.n24;
var a34:Number = a.n34; var b34:Number = b.n34;
var a44:Number = a.n44; var b44:Number = b.n44;
this.n11 = a11 * b11 + a12 * b21 + a13 * b31;
this.n12 = a11 * b12 + a12 * b22 + a13 * b32;
this.n13 = a11 * b13 + a12 * b23 + a13 * b33;
this.n14 = a11 * b14 + a12 * b24 + a13 * b34 + a14;
this.n21 = a21 * b11 + a22 * b21 + a23 * b31;
this.n22 = a21 * b12 + a22 * b22 + a23 * b32;
this.n23 = a21 * b13 + a22 * b23 + a23 * b33;
this.n24 = a21 * b14 + a22 * b24 + a23 * b34 + a24;
this.n31 = a31 * b11 + a32 * b21 + a33 * b31;
this.n32 = a31 * b12 + a32 * b22 + a33 * b32;
this.n33 = a31 * b13 + a32 * b23 + a33 * b33;
this.n34 = a31 * b14 + a32 * b24 + a33 * b34 + a34;
this.n41 = a41 * b11 + a42 * b21 + a43 * b31;
this.n42 = a41 * b12 + a42 * b22 + a43 * b32;
this.n43 = a41 * b13 + a42 * b23 + a43 * b33;
this.n44 = a41 * b14 + a42 * b24 + a43 * b34 + a44;
}
public static function multiply3x3( a:@ax-student-ar-org-papervision3d-core-math-Matrix3D, b:@ax-student-ar-org-papervision3d-core-math-Matrix3D ):@ax-student-ar-org-papervision3d-core-math-Matrix3D
{
//trace("Multiply3x3");
var m:@ax-student-ar-org-papervision3d-core-math-Matrix3D = new @ax-student-ar-org-papervision3d-core-math-Matrix3D();
m.calculateMultiply3x3( a, b );
return m;
}
public function calculateAdd( a:@ax-student-ar-org-papervision3d-core-math-Matrix3D, b:@ax-student-ar-org-papervision3d-core-math-Matrix3D ):void
{
this.n11 = a.n11 + b.n11;
this.n12 = a.n12 + b.n12;
this.n13 = a.n13 + b.n13;
this.n14 = a.n14 + b.n14;
this.n21 = a.n21 + b.n21;
this.n22 = a.n22 + b.n22;
this.n23 = a.n23 + b.n23;
this.n24 = a.n24 + b.n24;
this.n31 = a.n31 + b.n31;
this.n32 = a.n32 + b.n32;
this.n33 = a.n33 + b.n33;
this.n34 = a.n34 + b.n34;
}
public static function add( a:@ax-student-ar-org-papervision3d-core-math-Matrix3D, b:@ax-student-ar-org-papervision3d-core-math-Matrix3D ):@ax-student-ar-org-papervision3d-core-math-Matrix3D
{
//trace("matrix.add");
var m:@ax-student-ar-org-papervision3d-core-math-Matrix3D = new @ax-student-ar-org-papervision3d-core-math-Matrix3D();
m.calculateAdd( a, b );
return m;
}
public function calculateInverse( m:@ax-student-ar-org-papervision3d-core-math-Matrix3D ):void
{
var d:Number = m.det;
if( Math.abs(d) > 0.001 )
{
d = 1/d;
var m11:Number = m.n11; var m21:Number = m.n21; var m31:Number = m.n31;
var m12:Number = m.n12; var m22:Number = m.n22; var m32:Number = m.n32;
var m13:Number = m.n13; var m23:Number = m.n23; var m33:Number = m.n33;
var m14:Number = m.n14; var m24:Number = m.n24; var m34:Number = m.n34;
this.n11 = d * ( m22 * m33 - m32 * m23 );
this.n12 = -d * ( m12 * m33 - m32 * m13 );
this.n13 = d * ( m12 * m23 - m22 * m13 );
this.n14 = -d * ( m12 * (m23*m34 - m33*m24) - m22 * (m13*m34 - m33*m14) + m32 * (m13*m24 - m23*m14) );
this.n21 = -d * ( m21 * m33 - m31 * m23 );
this.n22 = d * ( m11 * m33 - m31 * m13 );
this.n23 = -d* ( m11 * m23 - m21 * m13 );
this.n24 = d * ( m11 * (m23*m34 - m33*m24) - m21 * (m13*m34 - m33*m14) + m31 * (m13*m24 - m23*m14) );
this.n31 = d * ( m21 * m32 - m31 * m22 );
this.n32 = -d* ( m11 * m32 - m31 * m12 );
this.n33 = d * ( m11 * m22 - m21 * m12 );
this.n34 = -d* ( m11 * (m22*m34 - m32*m24) - m21 * (m12*m34 - m32*m14) + m31 * (m12*m24 - m22*m14) );
}
}
public function calculateTranspose():void
{
var n11 :Number = this.n11;
var n12 :Number = this.n21;
var n13 :Number = this.n31;
var n14 :Number = this.n41;
var n21 :Number = this.n12;
var n22 :Number = this.n22;
var n23 :Number = this.n32;
var n24 :Number = this.n42;
var n31 :Number = this.n13;
var n32 :Number = this.n23;
var n33 :Number = this.n33;
var n34 :Number = this.n43;
var n41 :Number = this.n14;
var n42 :Number = this.n24;
var n43 :Number = this.n34;
var n44 :Number = this.n44;
this.n11 = n11; this.n12 = n12; this.n13 = n13; this.n14 = n14;
this.n21 = n21; this.n22 = n22; this.n23 = n23; this.n24 = n24;
this.n31 = n31; this.n32 = n32; this.n33 = n33; this.n34 = n34;
this.n41 = n41; this.n42 = n42; this.n43 = n43; this.n44 = n44;
}
public static function inverse( m:@ax-student-ar-org-papervision3d-core-math-Matrix3D ):@ax-student-ar-org-papervision3d-core-math-Matrix3D
{
var inv:@ax-student-ar-org-papervision3d-core-math-Matrix3D = new @ax-student-ar-org-papervision3d-core-math-Matrix3D();
inv.calculateInverse( m );
return inv;
}
public function invert() : void
{
temp.copy(this);
calculateInverse(temp);
}
public function get det():Number
{
return (this.n11 * this.n22 - this.n21 * this.n12) * this.n33 - (this.n11 * this.n32 - this.n31 * this.n12) * this.n23 +
(this.n21 * this.n32 - this.n31 * this.n22) * this.n13;
}
/*public function get trace():Number
{
return this.n11 + this.n22 + this.n33 + 1;
}*/
// _________________________________________________________________________________ COPY
public function copy( m:@ax-student-ar-org-papervision3d-core-math-Matrix3D ):@ax-student-ar-org-papervision3d-core-math-Matrix3D
{
this.n11 = m.n11; this.n12 = m.n12;
this.n13 = m.n13; this.n14 = m.n14;
this.n21 = m.n21; this.n22 = m.n22;
this.n23 = m.n23; this.n24 = m.n24;
this.n31 = m.n31; this.n32 = m.n32;
this.n33 = m.n33; this.n34 = m.n34;
return this;
}
public function copy3x3( m:@ax-student-ar-org-papervision3d-core-math-Matrix3D ):@ax-student-ar-org-papervision3d-core-math-Matrix3D
{
this.n11 = m.n11; this.n12 = m.n12; this.n13 = m.n13;
this.n21 = m.n21; this.n22 = m.n22; this.n23 = m.n23;
this.n31 = m.n31; this.n32 = m.n32; this.n33 = m.n33;
return this;
}
public static function clone( m:@ax-student-ar-org-papervision3d-core-math-Matrix3D ):@ax-student-ar-org-papervision3d-core-math-Matrix3D
{
//trace("matrix3D.clone");
return new @ax-student-ar-org-papervision3d-core-math-Matrix3D
(
[
m.n11, m.n12, m.n13, m.n14,
m.n21, m.n22, m.n23, m.n24,
m.n31, m.n32, m.n33, m.n34
]
);
}
// _________________________________________________________________________________ VECTOR
public static function multiplyVector( m:@ax-student-ar-org-papervision3d-core-math-Matrix3D, v:Number3D ):void
{
var vx:Number = v.x;
var vy:Number = v.y;
var vz:Number = v.z;
v.x = vx * m.n11 + vy * m.n12 + vz * m.n13 + m.n14;
v.y = vx * m.n21 + vy * m.n22 + vz * m.n23 + m.n24;
v.z = vx * m.n31 + vy * m.n32 + vz * m.n33 + m.n34;
}
public static function multiplyVector3x3( m:@ax-student-ar-org-papervision3d-core-math-Matrix3D, v:Number3D ):void
{
var vx:Number = v.x;
var vy:Number = v.y;
var vz:Number = v.z;
v.x = vx * m.n11 + vy * m.n12 + vz * m.n13;
v.y = vx * m.n21 + vy * m.n22 + vz * m.n23;
v.z = vx * m.n31 + vy * m.n32 + vz * m.n33;
}
public static function multiplyVector4x4( m:@ax-student-ar-org-papervision3d-core-math-Matrix3D, v:Number3D ):void
{
var vx:Number = v.x;
var vy:Number = v.y;
var vz:Number = v.z;
var vw:Number = 1.0 / (vx * m.n41 + vy * m.n42 + vz * m.n43 + m.n44);
v.x = vx * m.n11 + vy * m.n12 + vz * m.n13 + m.n14;
v.y = vx * m.n21 + vy * m.n22 + vz * m.n23 + m.n24;
v.z = vx * m.n31 + vy * m.n32 + vz * m.n33 + m.n34;
v.x *= vw;
v.y *= vw;
v.z *= vw;
}
public static function rotateAxis( m:@ax-student-ar-org-papervision3d-core-math-Matrix3D, v:Number3D ):void
{
var vx:Number = v.x;
var vy:Number = v.y;
var vz:Number = v.z;
v.x = vx * m.n11 + vy * m.n12 + vz * m.n13;
v.y = vx * m.n21 + vy * m.n22 + vz * m.n23;
v.z = vx * m.n31 + vy * m.n32 + vz * m.n33;
v.normalize();
}
/*
public static function projectVector( m:@ax-student-ar-org-papervision3d-core-math-Matrix3D, v:Number3D ):void
{
var c:Number = 1 / ( v.x * m.n41 + v.y * m.n42 + v.z * m.n43 + 1 );
multiplyVector( m, v );
v.x = v.x * c;
v.y = v.y * c;
v.z = 0;
}
*/
// _________________________________________________________________________________ EULER
/*
public static function matrix2eulerOLD( m:@ax-student-ar-org-papervision3d-core-math-Matrix3D ):Number3D
{
var angle:Number3D = new Number3D();
var d :Number = -Math.asin( Math.max( -1, Math.min( 1, m.n13 ) ) ); // Calculate Y-axis angle
var c :Number = Math.cos( d );
angle.y = d * toDEGREES;
var trX:Number, trY:Number;
if( Math.abs( c ) > 0.005 ) // Gimball lock?
{
trX = m.n33 / c; // No, so get X-axis angle
trY = -m.n23 / c;
angle.x = Math.atan2( trY, trX ) * toDEGREES;
trX = m.n11 / c; // Get Z-axis angle
trY = -m.n12 / c;
angle.z = Math.atan2( trY, trX ) * toDEGREES;
}
else // Gimball lock has occurred
{
angle.x = 0; // Set X-axis angle to zero
trX = m.n22; // And calculate Z-axis angle
trY = m.n21;
angle.z = Math.atan2( trY, trX ) * toDEGREES;
}
// TODO: Clamp all angles to range
return angle;
}
public static function matrix2euler2( t:@ax-student-ar-org-papervision3d-core-math-Matrix3D, rot:Number3D = null, scale:Number3D=null):Number3D
{
if(!rot) rot = Number3D.ZERO;
// Normalize the local x, y and z axes to remove scaling.
n3Di.reset( t.n11, t.n21, t.n31 );
n3Dj.reset( t.n12, t.n22, t.n32 );
n3Dk.reset( t.n13, t.n23, t.n33 );
n3Di.normalize();
n3Dj.normalize();
n3Dk.normalize();
temp.reset([
n3Di.x, n3Dj.x, n3Dk.x, 0,
n3Di.y, n3Dj.y, n3Dk.y, 0,
n3Di.z, n3Dj.z, n3Dk.z, 0
]);
var m:@ax-student-ar-org-papervision3d-core-math-Matrix3D = temp;
// Extract the first angle, rot.x
rot.x = Math.atan2( m.n23, m.n33 ); // rot.x = Math<T>::atan2 (M[1][2], M[2][2]);
// Remove the rot.x rotation from M, so that the remaining
// rotation, N, is only around two axes, and gimbal lock
// cannot occur.
var rx:@ax-student-ar-org-papervision3d-core-math-Matrix3D = @ax-student-ar-org-papervision3d-core-math-Matrix3D.rotationX( -rot.x );
var n:@ax-student-ar-org-papervision3d-core-math-Matrix3D = @ax-student-ar-org-papervision3d-core-math-Matrix3D.multiply( rx, m );
// Extract the other two angles, rot.y and rot.z, from N.
var cy:Number = Math.sqrt( n.n11 * n.n11 + n.n21 * n.n21); // T cy = Math<T>::sqrt (N[0][0]*N[0][0] + N[0][1]*N[0][1]);
rot.y = Math.atan2( -n.n31, cy ); // rot.y = Math<T>::atan2 (-N[0][2], cy);
rot.z = Math.atan2( -n.n12, n.n11 ); //rot.z = Math<T>::atan2 (-N[1][0], N[1][1]);
// Fix angles
if( rot.x == Math.PI )
{
if( rot.y > 0 )
rot.y -= Math.PI;
else
rot.y += Math.PI;
rot.x = 0;
rot.z += Math.PI;
}
// Convert to degrees if needed
// Shouldn't this have a check for Papervision3D.useDEGREES?
rot.x *= toDEGREES;
rot.y *= toDEGREES;
rot.z *= toDEGREES;
return rot;
}
*/
public static function matrix2euler( m :@ax-student-ar-org-papervision3d-core-math-Matrix3D, euler:Number3D=null, scale:Number3D=null ) : Number3D
{
euler = euler || new Number3D();
// need to get rid of scale
// TODO: whene scale is uniform, we can save some cycles. s = 3x3 determinant i beleive
var sx :Number = (scale && scale.x == 1) ? 1 : Math.sqrt(m.n11 * m.n11 + m.n21 * m.n21 + m.n31 * m.n31);
var sy :Number = (scale && scale.y == 1) ? 1 : Math.sqrt(m.n12 * m.n12 + m.n22 * m.n22 + m.n32 * m.n32);
var sz :Number = (scale && scale.z == 1) ? 1 : Math.sqrt(m.n13 * m.n13 + m.n23 * m.n23 + m.n33 * m.n33);
var n11 :Number = m.n11 / sx;
var n21 :Number = m.n21 / sy;
var n31 :Number = m.n31 / sz;
var n32 :Number = m.n32 / sz;
var n33 :Number = m.n33 / sz;
n31 = n31 > 1 ? 1 : n31;
n31 = n31 < -1 ? -1 : n31;
// zyx
euler.y = Math.asin(-n31);
euler.z = Math.atan2(n21, n11);
euler.x = Math.atan2(n32, n33);
// TODO: fix singularities
// yzx
//euler.z = Math.asin(-m.n21);
//euler.y = Math.atan2(m.n31, m.n11);
//euler.x = Math.atan2(-m.n23, m.n22);
// zxy
//euler.x = Math.asin(-m.n32);
//euler.z = Math.atan2(-m.n12, m.n22);
//euler.y = Math.atan2(-m.n31, m.n33);
if(Papervision3D.useDEGREES)
{
euler.x *= toDEGREES;
euler.y *= toDEGREES;
euler.z *= toDEGREES;
}
// Clamp values
// euler.x = euler.x < 0 ? euler.x + 360 : euler.x;
// euler.y = euler.y < 0 ? euler.y + 360 : euler.y;
// euler.z = euler.z < 0 ? euler.z + 360 : euler.z;
return euler;
}
public static function euler2matrix( deg:Number3D ):@ax-student-ar-org-papervision3d-core-math-Matrix3D
{
//trace("euler2matrix");
temp.reset();
var m:@ax-student-ar-org-papervision3d-core-math-Matrix3D = temp;
m = temp;
var ax:Number = deg.x * toRADIANS;
var ay:Number = deg.y * toRADIANS;
var az:Number = deg.z * toRADIANS;
var a:Number = Math.cos( ax );
var b:Number = Math.sin( ax );
var c:Number = Math.cos( ay );
var d:Number = Math.sin( ay );
var e:Number = Math.cos( az );
var f:Number = Math.sin( az );
var ad:Number = a * d;
var bd:Number = b * d;
m.n11 = c * e;
m.n12 = -c * f;
m.n13 = d;
m.n21 = bd * e + a * f;
m.n22 = -bd * f + a * e;
m.n23 = -b * c;
m.n31 = -ad * e + b * f;
m.n32 = ad * f + b * e;
m.n33 = a * c;
return m;
}
// _________________________________________________________________________________ ROTATION
public static function rotationX( rad:Number ):@ax-student-ar-org-papervision3d-core-math-Matrix3D
{
//trace("rotationX");
var m :@ax-student-ar-org-papervision3d-core-math-Matrix3D = IDENTITY;
var c :Number = Math.cos( rad );
var s :Number = Math.sin( rad );
m.n22 = c;
m.n23 = -s;
m.n32 = s;
m.n33 = c;
return m;
}
public static function rotationY( rad:Number ):@ax-student-ar-org-papervision3d-core-math-Matrix3D
{
//trace("rotationY");
var m :@ax-student-ar-org-papervision3d-core-math-Matrix3D = IDENTITY;
var c :Number = Math.cos( rad );
var s :Number = Math.sin( rad );
m.n11 = c;
m.n13 = -s;
m.n31 = s;
m.n33 = c;
return m;
}
public static function rotationZ( rad:Number ):@ax-student-ar-org-papervision3d-core-math-Matrix3D
{
//trace("rotationZ");
var m :@ax-student-ar-org-papervision3d-core-math-Matrix3D = IDENTITY;
var c :Number = Math.cos( rad );
var s :Number = Math.sin( rad );
m.n11 = c;
m.n12 = -s;
m.n21 = s;
m.n22 = c;
return m;
}
public static function rotationMatrix( x:Number, y:Number, z:Number, rad:Number, targetmatrix:@ax-student-ar-org-papervision3d-core-math-Matrix3D = null ):@ax-student-ar-org-papervision3d-core-math-Matrix3D
{
var m:@ax-student-ar-org-papervision3d-core-math-Matrix3D;
if(!targetmatrix)
{
//trace("rotationmatrix");
m = IDENTITY;
}
else m = targetmatrix;
var nCos:Number = Math.cos( rad );
var nSin:Number = Math.sin( rad );
var scos:Number = 1 - nCos;
var sxy :Number = x * y * scos;
var syz :Number = y * z * scos;
var sxz :Number = x * z * scos;
var sz :Number = nSin * z;
var sy :Number = nSin * y;
var sx :Number = nSin * x;
m.n11 = nCos + x * x * scos;
m.n12 = -sz + sxy;
m.n13 = sy + sxz;
m.n14 = 0;
m.n21 = sz + sxy;
m.n22 = nCos + y * y * scos;
m.n23 = -sx + syz;
m.n24 = 0;
m.n31 = -sy + sxz;
m.n32 = sx + syz;
m.n33 = nCos + z * z * scos;
m.n34 = 0;
return m;
}
public static function rotationMatrixWithReference( axis:Number3D, rad:Number, ref:Number3D ):@ax-student-ar-org-papervision3d-core-math-Matrix3D
{
var m:@ax-student-ar-org-papervision3d-core-math-Matrix3D = @ax-student-ar-org-papervision3d-core-math-Matrix3D.translationMatrix( ref.x, -ref.y, ref.z );
m.calculateMultiply( m, @ax-student-ar-org-papervision3d-core-math-Matrix3D.rotationMatrix( axis.x, axis.y, axis.z, rad ) );
m.calculateMultiply( m, @ax-student-ar-org-papervision3d-core-math-Matrix3D.translationMatrix ( -ref.x, ref.y, -ref.z ) );
return m;
}
// _________________________________________________________________________________ TRANSFORM
public static function translationMatrix( x:Number, y:Number, z:Number ):@ax-student-ar-org-papervision3d-core-math-Matrix3D
{
//trace("translation matrix");
var m:@ax-student-ar-org-papervision3d-core-math-Matrix3D = IDENTITY;
m.n14 = x;
m.n24 = y;
m.n34 = z;
return m;
}
public static function scaleMatrix( x:Number, y:Number, z:Number ):@ax-student-ar-org-papervision3d-core-math-Matrix3D
{
//trace("scalematrix");
var m:@ax-student-ar-org-papervision3d-core-math-Matrix3D = IDENTITY;
m.n11 = x;
m.n22 = y;
m.n33 = z;
return m;
}
// _________________________________________________________________________________ QUATERNIONS
public static function magnitudeQuaternion( q:Object ):Number
{
return( Math.sqrt( q.w * q.w + q.x * q.x + q.y * q.y + q.z * q.z ) );
}
public static function normalizeQuaternion( q:Object ):Object
{
var mag:Number = magnitudeQuaternion( q );
q.x /= mag;
q.y /= mag;
q.z /= mag;
q.w /= mag;
return q;
}
public static function axis2quaternion( x:Number, y:Number, z:Number, angle:Number ):Object
{
var sin:Number = Math.sin( angle / 2 );
var cos:Number = Math.cos( angle / 2 );
var q:Object = new Object();
q.x = x * sin;
q.y = y * sin;
q.z = z * sin;
q.w = cos;
return normalizeQuaternion( q );
}
public static function euler2quaternion( ax:Number, ay:Number, az:Number, targetquat:Quaternion = null ):Quaternion
{
var fSinPitch :Number = Math.sin( ax * 0.5 );
var fCosPitch :Number = Math.cos( ax * 0.5 );
var fSinYaw :Number = Math.sin( ay * 0.5 );
var fCosYaw :Number = Math.cos( ay * 0.5 );
var fSinRoll :Number = Math.sin( az * 0.5 );
var fCosRoll :Number = Math.cos( az * 0.5 );
var fCosPitchCosYaw :Number = fCosPitch * fCosYaw;
var fSinPitchSinYaw :Number = fSinPitch * fSinYaw;
var q:Quaternion;
if(!targetquat) q = new Quaternion();
else q = targetquat;
q.x = fSinRoll * fCosPitchCosYaw - fCosRoll * fSinPitchSinYaw;
q.y = fCosRoll * fSinPitch * fCosYaw + fSinRoll * fCosPitch * fSinYaw;
q.z = fCosRoll * fCosPitch * fSinYaw - fSinRoll * fSinPitch * fCosYaw;
q.w = fCosRoll * fCosPitchCosYaw + fSinRoll * fSinPitchSinYaw;
return q;
}
// TODO (LOW) rewrite so that this takes an actual Quaternion object
public static function quaternion2matrix( x:Number, y:Number, z:Number, w:Number, targetmatrix:@ax-student-ar-org-papervision3d-core-math-Matrix3D = null ):@ax-student-ar-org-papervision3d-core-math-Matrix3D
{
var xx:Number = x * x;
var xy:Number = x * y;
var xz:Number = x * z;
var xw:Number = x * w;
var yy:Number = y * y;
var yz:Number = y * z;
var yw:Number = y * w;
var zz:Number = z * z;
var zw:Number = z * w;
var m:@ax-student-ar-org-papervision3d-core-math-Matrix3D;
if(!targetmatrix)
{
//trace("quat to matrix");
m = IDENTITY;
}
else
{
m = targetmatrix ;
}
m.n11 = 1 - 2 * ( yy + zz );
m.n12 = 2 * ( xy - zw );
m.n13 = 2 * ( xz + yw );
m.n21 = 2 * ( xy + zw );
m.n22 = 1 - 2 * ( xx + zz );
m.n23 = 2 * ( yz - xw );
m.n31 = 2 * ( xz - yw );
m.n32 = 2 * ( yz + xw );
m.n33 = 1 - 2 * ( xx + yy );
return m;
}
public static function multiplyQuaternion( a:Object, b:Object ):Object
{
var ax:Number = a.x; var ay:Number = a.y; var az:Number = a.z; var aw:Number = a.w;
var bx:Number = b.x; var by:Number = b.y; var bz:Number = b.z; var bw:Number = b.w;
var q:Object = new Object();
q.x = aw*bx + ax*bw + ay*bz - az*by;
q.y = aw*by + ay*bw + az*bx - ax*bz;
q.z = aw*bz + az*bw + ax*by - ay*bx;
q.w = aw*bw - ax*bx - ay*by - az*bz;
return q;
}
// _________________________________________________________________________________ TRIG
static private var toDEGREES :Number = 180/Math.PI;
static private var toRADIANS :Number = Math.PI/180;
static private var _sin:Function = Math.sin;
static private var _cos:Function = Math.cos;
}}
(C) Æliens
04/09/2009
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